I am afraid that is not answering the question originally asked ...which is heading all our contributions ... basically it is the amount of lens movement before one looses acceptable focus, the size of the CoC produced ... movement which is less at close distances than at far distance. In my first drawing if red was the focus then there would be another line meeting at about twice the blue-red distance drawn ... assuming the 33/66% balance. So the reverse is true that the angle is so small at far distances it takes a greater change to go beyond the acceptable CoC than at closer distances. Hence we have greater DoF at distance than when close and I think the angles involved are the 'why' of what is the 'what'. The refraction remains the same but it requires greater differences in distance to go out of focus way out than close in.

As the subject moves away the angle to the circumfrance of the lens is smaller so the complimentary angle behind the lens is greater helping to keep it is focus ... a different way of saying the same thing

As Dan said it is basically geometry.